Question

in an AP the first term is -4 and last term is 29 and the sum of all time the terms is 150 find the common difference of the AP

Answer 1

Given
A=-4
L=29
Sn=150
Using formula,
Sn=n/2(a+l)
150=n/2(-4+29)
150=n/2(25)
25n=300
n=12
Now,
Then common difference=3

Answer 2

Answer:

$3=d$

Step-by-step explanation:

First term = a = -4

$a_n=29$

Sum of n terms = $\frac{n}{2}(a+a_n)$

Since we are given that the sum of all terms is 150

So, $150=\frac{n}{2}(-4+29)$

$150 \times 2=25n$

$300=25n$

$\frac{300}{25}=n$

$12=n$

Formula of nth term = $a_n=a+(n-1)d$

Where d is the common difference

Substitute n =12

So,  $a_{12}=a+(12-1)d$

$29=-4+11d$

$29+4=11d$

$\frac{33}{11}=d$

$3=d$

Hence the common difference is 3